DONETSK, Ukraine—When international observers arrived for the first time at the Flight 17 crash site outside this separatist-held capital on Friday afternoon, they found what they described as a field of already decomposing body parts and debris, lacking a secure cordon or any discernible on-site management. It was guarded by armed irregulars, some of whom the observers accused of being drunk.

The visit of monitors from the Organization for Security and Cooperation in Europe, limited to 75 minutes and two areas of debris,...